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In this paper, we present fixed point theorems for a generalized Roger Hardy type F-contraction in metric-like spaces and also give some examples to illustrate the main results in this paper. Moreover the applications of second-order differential equations and fractional differential equations are shown. The existing results improve and extend the corresponding results in the literature.

In this paper, we have proved the degree of approximation of functions belonging to $ L[0, \infty ) $ by Harmonic-Euler means of its Fourier-Laguerre series at $ x = 0 $. The aim of this paper is to concentrate on the approximation properties of the functions in $ L[0, \infty ) $ by Harmonic-Euler means of its Fourier-Laguerre series associated with the function f.

In this paper, a residual power series method (RPSM) is combining Taylor’s formula series with residual error function, and is investigated to find a novel analytical solution of the coupled strong system nonlinear Boussinesq-Burgers equations according to the time. Analytical solution was purposed to find approximate solutions by RPSM and compared with the exact solutions and approximate solutions obtained by the homotopy perturbation method and optimal homotopy asymptotic method at different time and concluded that the present results are more accurate and efficient than analytical methods studied. Then, analytical simulations of the results are studied graphically through representations for action of time and accuracy of method.

In this paper, first, we derive the operational matrix of two-dimensional orthogonal triangular functions (2D-TFs) for two-dimensional fractional integrals. Then, we apply this operational matrix and properties of Two-dimensional orthogonal triangular functions to reduce two-dimensional fractional integral equations to a system of algebraic equations. Finally, in order to show the validity and efficiency, we present some numerical examples.

In this paper, we give new necessary and sufficient conditions for the asymptotic stability of a linear delay difference system: $ x_{n+1}-ax_{n}-Ax_{n-k}=0 $, where A is a $ 2\times 2 $ constant matrix, k is a nonnegative integer and a is a real number. To prove the theorems, root analysis is used for characteristic equation of system.

The present work examines the finite difference modeling of SH-wave in a multilayered orthotropic crust to perceive the stability criterion and dispersion equation. The dispersion equation, for the case when $ (n-1) $ layers underlying the earth or along its surface, is obtained in a standard form. This paper actually assigns to apply the finite difference method in seismic wave propagation. The phase and group velocity are retrieved utilizing the techniques of finite difference method. For the occurrence of SH-wave propagation, stability conditions are constituted applying the technique of finite difference method in time and space. The graphs are produced to comprehend the concepts of dispersion equation, group velocity, and phase velocity.

In this paper, we numerically study a dynamic viscoelastic problem. The variational formulation is written as a linear parabolic variational equation for the velocity field. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced using the implicit Euler scheme and the finite element method, for which some a priori error estimates are derived, leading to the linear convergence of the algorithm under suitable additional regularity conditions. Finally, some one- and three-dimensional numerical simulations are presented to show the accuracy of the algorithm and the behaviour of the solution, including a comparison with an experimental study.

In this paper CR-warped product submanifolds of a generalized complex space form are studied and a characterizing inequality for existence of CR-warped product submanifolds is established. Moreover, some special cases are also discussed.

In this paper, we prove a version of the Hadamard inequality for function f such that $ f^{(n)} $ is convex via k-fractional Caputo derivatives. Using convexity of $ |f^{(n)}|^q $, $ q \ge 1 $ we find the bounds of the difference of fractional differential inequality. Also we have found inequalities for Caputo fractional derivatives.

In the paper, the authors introduce a new concept “extended $ ((s_1,m_1) $-$ (s_2,m_2)) $-convex function on co-ordinates” and establish some new inequalities of the Hermite–Hadamard type for extended $ ((s_1,m_1) $-$ (s_2,m_2)) $-convex functions of 2 variables on co-ordinates.

In this paper, approximate controllability of an abstract semilinear control system is proved under simple sufficient conditions in Hilbert spaces. The results are obtained when nonlinearity satisfy Lipschitz condition. At the end one example is given to illustrate the results.

The problem of geometric flow and determining the eigenvalues for nonlinear operators acting on finite-dimensional manifolds is a known problem. In this paper we will consider the eigenvalue problem for the p-Laplace operator acting on the space of functions on closed manifolds. We find the first variation formula for the eigenvalues of p-Laplacian on a closed manifold evolving by the Yamabe flow and find some applications.

In this paper, we present a Picard’s iterative method for the solution of nonlinear multicomponent transport equations. The multicomponent transport equations are important for mixture models of the ionized and neutral particles in plasma simulations. Such mixtures deal with the so-called Stefan–Maxwell approaches for the multicomponent diffusion. The underlying nonlinearities are delicate and it is not necessary to be an analytical function of the dependent variables. The proposed solver method is based on Banach’s contraction fix-point principle that allows to solve such nonlinearities without making any use to Lagrange multipliers and constrained variations. Such an improvement allows to solve delicate nonlinear problems and we test the application to model with multicomponent transport equations.

In this paper we study a periodic boundary value problem of first order nonlinear differential equations with maxima and discuss the existence and approximation of the solutions. The main result relies on the Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. At the end, we give an example to illustrate the applicability of the abstract results to some concrete periodic boundary value problems of nonlinear differential equations.

In this paper we find conditions for boundedness of self-map composition operators on weighted spaces of holomorphic functions on the upper half-plane for two kinds of weights which are of moderate growth.

In this paper we combined two well-known analytical methods: the homotopy analysis method (HAM) and the method of integral (invariant) manifold to investigate the problems of auto-ignition of a polydisperse fuel spray. We call this combination the singular perturbed homotopy analysis method (SPHAM). In many cases, combustion processes are described by mathematical models that include a set of highly nonlinear differential equations that are characterized by a different time scale (so-called multi-scale systems). For example, the temperature is a fast variable, due to the Arrhenius factor, compared to the radius evolution variable (the evaporation process). We apply the SPHAM method to problems of thermal explosion in two-phase combustible mixtures of gas with polydisperse fuel droplets. We analyze a dependence of our analytical and/or numerical results for different practical probabilistic distributions of fuel droplets, that are modeled by continuous probability distribution functions. By applying the SPHAM, we derived an analytical solution of the system for comparatively simple models of thermal explosion and compared our results with numerical simulations.

In the present paper, we investigate upper bounds on the third Hankel determinants for the starlike and convex functions with respect to symmetric points in the open unit disk.

In the paper, the authors establish some new Hermite–Hadamard type inequalities for differentiable co-ordinated convex functions of two variables.

The Hankel determinant appears in representations of solutions to several integrable systems. An asymptotic expansion of the Hankel determinant thus plays a key role in the investigation of asymptotic analysis of such integrable systems. This paper presents an asymptotic expansion formula of a certain Casorati determinant as an extension of the Hankel case. This Casorati determinant is then shown to be associated with the solution to the discrete hungry Lotka–Volterra (dhLV) system, which is an integrable variant of the famous prey–predator model in mathematical biology. Finally, the asymptotic behavior of the dhLV system is clarified using the expansion formula for the Casorati determinant.